{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5c18e767-dda0-4141-a219-a5195272c64a",
   "metadata": {},
   "source": [
    "Chapter 27\n",
    "# 一元概率密度估计\n",
    "Book_1《编程不难》 | 鸢尾花书：从加减乘除到机器学习  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "14171c17-ddbc-4b1e-a459-2fea7a2a03da",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt \n",
    "import pandas as pd  \n",
    "from sklearn.datasets import load_iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "02ff6f44-ede1-41cb-81eb-b5546436f6c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 从Scikit-Learn库加载鸢尾花数据\n",
    "iris = load_iris()\n",
    "y = iris.target\n",
    "X_df = pd.DataFrame(iris.data)\n",
    "X1_df = X_df.iloc[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b0f9afba-2ee5-49fa-9d53-4edf49f6e2d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 自定义可视化函数\n",
    "def visualize(x1,pdf,color):\n",
    "    fig, ax = plt.subplots(figsize = (8,3))\n",
    "    ax.fill_between(x1, pdf, \n",
    "                    facecolor = color,alpha = 0.2)\n",
    "    ax.plot(x1, pdf,color = color)\n",
    "\n",
    "    ax.set_ylim([0,1.4])\n",
    "    ax.set_xlim([4,8])\n",
    "    ax.set_ylabel('PDF')\n",
    "    ax.set_xlabel('Sepal length, $x_1$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ea2ddee5-879d-4ad4-b3ea-192686b344e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<statsmodels.nonparametric.kde.KDEUnivariate at 0x2ec8a543970>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 不考虑标签\n",
    "KDE = sm.nonparametric.KDEUnivariate(X1_df)\n",
    "KDE.fit(bw=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e12f1b0c-157f-4bc1-9624-05dcd2b60a46",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.linspace(4,8,101)\n",
    "f_x1 = KDE.evaluate(x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a1714838-60aa-49ee-8ec8-c3af0bb980a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "visualize(x1,f_x1,'#00448A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a3e56291-0420-4f68-a5b1-b8dcc759cefb",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 考虑鸢尾花标签，用KDE描述样本数据花萼长度分布\n",
    "colors = ['#FF3300','#0099FF','#8A8A8A']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3bb1a1ec-9998-4372-8c9a-d9c3cd49874f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.linspace(4,8,161)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "65283440-8761-47be-8e73-0240faf06829",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for idx in range(3):\n",
    "    KDE_C_i = sm.nonparametric.KDEUnivariate(X1_df[y==idx])\n",
    "    KDE_C_i.fit(bw=0.1)\n",
    "    f_x1_given_C_i = KDE_C_i.evaluate(x1)\n",
    "    \n",
    "    visualize(x1,f_x1_given_C_i,colors[idx])"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
